The Planted $k$-SUM Problem: Algorithms, Lower Bounds, Hardness Amplification, and Cryptography

ePrint Report: The Planted $k$-SUM Problem: Algorithms, Lower Bounds, Hardness Amplification, and Cryptography

Sagnik Saha, Nikolaj Ignatieff Schwartzbach, Prashant Nalini Vasudevan

In the average-case $k$-SUM problem, given $r$ integers chosen uniformly at random from $\{0,\ldots,M-1\}$, the objective is to find a set of $k$ numbers that sum to 0 modulo $M$ (this set is called a "solution"). In the related $k$-XOR problem, given $k$ uniformly random Boolean vectors of length log $M$, the objective is to find a set of …

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